Algebra Examples

$- 2 x - 3 \leq y$ $y - 1 < \frac{1}{2} x$

Step 1

Graph $- 2 x - 3 \leq y$ .

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Step 1.1

Rewrite so $y$ is on the left side of the inequality.

$y \geq - 2 x - 3$

Step 1.2

Use the slope-intercept form to find the slope and y-intercept.

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Step 1.2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 2$

$b = - 3$

Step 1.2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 2$

y-intercept: $(0, - 3)$

Slope: $- 2$

y-intercept: $(0, - 3)$

Step 1.3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- 2 x - 3$ .

$y \geq - 2 x - 3$

Step 2

Graph $y - 1 < \frac{1}{2} x$ .

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Step 2.1

Write in $y = m x + b$ form.

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Step 2.1.1

Solve for $y$ .

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Step 2.1.1.1

Simplify $\frac{1}{2} x$ .

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Step 2.1.1.1.1

Rewrite.

$y - 1 < 0 + 0 + \frac{1}{2} x$

Step 2.1.1.1.2

Simplify by adding zeros.

$y - 1 < \frac{1}{2} x$

Step 2.1.1.1.3

Combine $\frac{1}{2}$ and $x$ .

$y - 1 < \frac{x}{2}$

Step 2.1.1.2

Add $1$ to both sides of the inequality.

$y < \frac{x}{2} + 1$

Step 2.1.2

Reorder terms.

$y < \frac{1}{2} x + 1$

Step 2.2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{1}{2}$

$b = 1$

Step 2.2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Step 2.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x + 1$ .

$y < \frac{1}{2} x + 1$

Step 3

Plot each graph on the same coordinate system.

$- 2 x - 3 \leq y$

$y - 1 < \frac{1}{2} x$

Step 4